\section{mSHAKE of CH}
\begin{equation}
A_{CH}=
\left[\begin{matrix}r^{uc}_{01} r_{01} \left(\frac{1}{m_{1}} + \frac{1}{m_{0}}\right)\end{matrix}\right]
\end{equation}
\begin{equation}
c_{CH}=
\left[\begin{matrix}\frac{- d_{01}^{2} + \left(r^{uc}_{01}\right)^{2}}{4 \varDelta{t}^{2}}\end{matrix}\right]
\end{equation}
\begin{align}
q_0 &=
\frac{l_{0}^{2} r_{01}^{2} \left(m_{0} + m_{1}\right)^{2}}{m_{0}^{2} m_{1}^{2}}
\end{align}
\section{mSHAKE of CH2}
\begin{equation}
A_{CH2}=
\left[\begin{matrix}r^{uc}_{01} r_{01} \left(\frac{1}{m_{1}} + \frac{1}{m_{0}}\right) & \frac{r^{uc}_{01} r_{02}}{m_{0}}\\\frac{r^{uc}_{02} r_{01}}{m_{0}} & r^{uc}_{02} r_{02} \left(\frac{1}{m_{2}} + \frac{1}{m_{0}}\right)\end{matrix}\right]
\end{equation}
\begin{equation}
c_{CH2}=
\left[\begin{matrix}\frac{- d_{01}^{2} + \left(r^{uc}_{01}\right)^{2}}{4 \varDelta{t}^{2}}\\\frac{- d_{02}^{2} + \left(r^{uc}_{02}\right)^{2}}{4 \varDelta{t}^{2}}\end{matrix}\right]
\end{equation}
\begin{align}
q_0 &=
\frac{l_{0}^{2} r_{01}^{2} \left(m_{0} + m_{1}\right)^{2} + 2 l_{0} l_{1} m_{1} r_{01} r_{02} \left(m_{0} + m_{1}\right) + l_{1}^{2} m_{1}^{2} r_{02}^{2}}{m_{0}^{2} m_{1}^{2}}
\\
q_1 &=
\frac{l_{0}^{2} m_{2}^{2} r_{01}^{2} + 2 l_{0} l_{1} m_{2} r_{01} r_{02} \left(m_{0} + m_{2}\right) + l_{1}^{2} r_{02}^{2} \left(m_{0} + m_{2}\right)^{2}}{m_{0}^{2} m_{2}^{2}}
\end{align}
\section{mSHAKE of OH2}
\begin{equation}
A_{OH2}=
\left[\begin{matrix}r^{uc}_{01} r_{01} \left(\frac{1}{m_{1}} + \frac{1}{m_{0}}\right) & \frac{r^{uc}_{01} r_{02}}{m_{0}} & - \frac{r^{uc}_{01} r_{12}}{m_{1}}\\\frac{r^{uc}_{02} r_{01}}{m_{0}} & r^{uc}_{02} r_{02} \left(\frac{1}{m_{2}} + \frac{1}{m_{0}}\right) & \frac{r^{uc}_{02} r_{12}}{m_{2}}\\- \frac{r^{uc}_{12} r_{01}}{m_{1}} & \frac{r^{uc}_{12} r_{02}}{m_{2}} & r^{uc}_{12} r_{12} \left(\frac{1}{m_{2}} + \frac{1}{m_{1}}\right)\end{matrix}\right]
\end{equation}
\begin{equation}
c_{OH2}=
\left[\begin{matrix}\frac{- d_{01}^{2} + \left(r^{uc}_{01}\right)^{2}}{4 \varDelta{t}^{2}}\\\frac{- d_{02}^{2} + \left(r^{uc}_{02}\right)^{2}}{4 \varDelta{t}^{2}}\\\frac{- d_{12}^{2} + \left(r^{uc}_{12}\right)^{2}}{4 \varDelta{t}^{2}}\end{matrix}\right]
\end{equation}
\begin{align}
q_0 &=
\frac{l_{0}^{2} r_{01}^{2} \left(m_{0} + m_{1}\right)^{2} + 2 l_{0} l_{1} m_{1} r_{01} r_{02} \left(m_{0} + m_{1}\right) - 2 l_{0} l_{2} m_{0} r_{01} r_{12} \left(m_{0} + m_{1}\right) + l_{1}^{2} m_{1}^{2} r_{02}^{2} - 2 l_{1} l_{2} m_{0} m_{1} r_{02} r_{12} + l_{2}^{2} m_{0}^{2} r_{12}^{2}}{m_{0}^{2} m_{1}^{2}}
\\
q_1 &=
\frac{l_{0}^{2} m_{2}^{2} r_{01}^{2} + 2 l_{0} l_{1} m_{2} r_{01} r_{02} \left(m_{0} + m_{2}\right) + 2 l_{0} l_{2} m_{0} m_{2} r_{01} r_{12} + l_{1}^{2} r_{02}^{2} \left(m_{0} + m_{2}\right)^{2} + 2 l_{1} l_{2} m_{0} r_{02} r_{12} \left(m_{0} + m_{2}\right) + l_{2}^{2} m_{0}^{2} r_{12}^{2}}{m_{0}^{2} m_{2}^{2}}
\\
q_2 &=
\frac{l_{0}^{2} m_{2}^{2} r_{01}^{2} - 2 l_{0} l_{1} m_{1} m_{2} r_{01} r_{02} - 2 l_{0} l_{2} m_{2} r_{01} r_{12} \left(m_{1} + m_{2}\right) + l_{1}^{2} m_{1}^{2} r_{02}^{2} + 2 l_{1} l_{2} m_{1} r_{02} r_{12} \left(m_{1} + m_{2}\right) + l_{2}^{2} r_{12}^{2} \left(m_{1} + m_{2}\right)^{2}}{m_{1}^{2} m_{2}^{2}}
\end{align}
\section{mSHAKE of CH3}
\begin{equation}
A_{CH3}=
\left[\begin{matrix}r^{uc}_{01} r_{01} \left(\frac{1}{m_{1}} + \frac{1}{m_{0}}\right) & \frac{r^{uc}_{01} r_{02}}{m_{0}} & \frac{r^{uc}_{01} r_{03}}{m_{0}}\\\frac{r^{uc}_{02} r_{01}}{m_{0}} & r^{uc}_{02} r_{02} \left(\frac{1}{m_{2}} + \frac{1}{m_{0}}\right) & \frac{r^{uc}_{02} r_{03}}{m_{0}}\\\frac{r^{uc}_{03} r_{01}}{m_{0}} & \frac{r^{uc}_{03} r_{02}}{m_{0}} & r^{uc}_{03} r_{03} \left(\frac{1}{m_{3}} + \frac{1}{m_{0}}\right)\end{matrix}\right]
\end{equation}
\begin{equation}
c_{CH3}=
\left[\begin{matrix}\frac{- d_{01}^{2} + \left(r^{uc}_{01}\right)^{2}}{4 \varDelta{t}^{2}}\\\frac{- d_{02}^{2} + \left(r^{uc}_{02}\right)^{2}}{4 \varDelta{t}^{2}}\\\frac{- d_{03}^{2} + \left(r^{uc}_{03}\right)^{2}}{4 \varDelta{t}^{2}}\end{matrix}\right]
\end{equation}
\begin{align}
q_0 &=
\frac{l_{0}^{2} r_{01}^{2} \left(m_{0} + m_{1}\right)^{2} + 2 l_{0} m_{1} r_{01} \left(m_{0} + m_{1}\right) \left(l_{1} r_{02} + l_{2} r_{03}\right) + m_{1}^{2} \left(l_{1}^{2} r_{02}^{2} + 2 l_{1} l_{2} r_{02} r_{03} + l_{2}^{2} r_{03}^{2}\right)}{m_{0}^{2} m_{1}^{2}}
\\
q_1 &=
\frac{l_{1}^{2} r_{02}^{2} \left(m_{0} + m_{2}\right)^{2} + 2 l_{1} m_{2} r_{02} \left(m_{0} + m_{2}\right) \left(l_{0} r_{01} + l_{2} r_{03}\right) + m_{2}^{2} \left(l_{0}^{2} r_{01}^{2} + 2 l_{0} l_{2} r_{01} r_{03} + l_{2}^{2} r_{03}^{2}\right)}{m_{0}^{2} m_{2}^{2}}
\\
q_2 &=
\frac{l_{2}^{2} r_{03}^{2} \left(m_{0} + m_{3}\right)^{2} + 2 l_{2} m_{3} r_{03} \left(m_{0} + m_{3}\right) \left(l_{0} r_{01} + l_{1} r_{02}\right) + m_{3}^{2} \left(l_{0}^{2} r_{01}^{2} + 2 l_{0} l_{1} r_{01} r_{02} + l_{1}^{2} r_{02}^{2}\right)}{m_{0}^{2} m_{3}^{2}}
\end{align}
